Seminars: P. A. Borodin, Approximations by simple partial fractions with constraints on the poles

SEMINARS


Seminar on Complex Analysis (Gonchar Seminar) February 9, 2015 18:00, Moscow, Steklov Mathematical Institute, Room 411 (8 Gubkina)

Approximations by simple partial fractions with constraints on the poles P. A. Borodin M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Abstract: We discusss the following new result: if the plane compact set $K$ has connected complement and is covered by the union $\widehat{E}\setminus E$ of bounded components of complement of another compact set $E$, then the simple partial fractions (logarithmic derivatives of polynomials) having all poles on $E$ are dense in the space $AC(K)$ of functions that are continuous on $K$ and analytic on its interior.